| 抛物型微分方程的Crank-Nicolson块中心差分方法 |
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| 引用本文： | 任宗修,张秀春,银召利.抛物型微分方程的Crank-Nicolson块中心差分方法[J].河南师范大学学报(自然科学版),2011,39(1):15-19. |
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| 作者姓名： | 任宗修 张秀春 银召利 |
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| 作者单位： | 河南师范大学,数学与信息科学学院,河南,新乡,453007 |
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| 摘 要： | 针对有界区域上的抛物型微分方程讨论了Crank-Nicolson块中心差分法, 在非等距剖分的网格上得了近似解和解的一阶导数的L2模误差估计,重要的是提高了时间上的精度. 数值试验结果与理论分析一致,说明格式具有高效的收敛性.
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| 关 键 词： | 抛物型微分方程 Crank-Nicolson 块中心差分方法 误差估计 |
Crank-Nicolson Block-centered Difference Scheme For Parabolic Problems |
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| REN Zong-xiu,ZHANG Xiu-chun,YIN zhao-li.Crank-Nicolson Block-centered Difference Scheme For Parabolic Problems[J].Journal of Henan Normal University(Natural Science),2011,39(1):15-19. |
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| Authors: | REN Zong-xiu ZHANG Xiu-chun YIN zhao-li |
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| Institution: | (College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China) |
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| Abstract: | This paper considers the Crank-Nicolson block-centered difference method for the solution of the linear parabolic differential problems in the bounded domain.The research gets the discrete L2-norm errors in both the approximate solution and its first derivatives for all nonuniform grids,with sufficiently smooth data.It is important to get higher precision in time than the block-centered finite difference method.It is the same time to have the same result in the numerical experiment and the theorem. |
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| Keywords: | parabolic differential equation Crank-Nicolson block-centered differences method error estimates |
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